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Abstract

Metallic nanoparticles arranged in arrays have been shown to support both localized surface plasmons (LSPs) and diffractive grating behavior, related to the inter-particle period. By selecting both the period and particle size, it is possible to generate lattice modes that are caused by interference of the LSP and the grating Rayleigh anomaly. These hybrid modes show a Fano-like lineshape with reduced linewidth relative to the LSP mode. In this paper, we study the lattice modes supported by gold and aluminum nanoparticle arrays in the visible and UV, both experimentally and theoretically. The measured and simulated dispersion curves allow us to comprehensively analyze the details of the LSP coupling in the array. We show that when the spectral position of the Rayleigh anomaly, dependent on the period of the array, is slightly blue-shifted with respect to the LSP resonance, the quality factor of the lattice mode is significantly increased. We also provide evidence that the formation of the lattice modes critically depends on the incident light polarization, with maximum coupling efficiency between LSPs and the in-plane scattered light when the polarization direction is perpendicular to the propagation direction of the grazing wave. The results obtained provide design rules for high quality factor resonances throughout the visible and ultraviolet spectral ranges.

Figures (8)

(a) Schematic of the considered geometry: an array of metal nanoparticles deposited onto a dielectric substrate of refractive index n1. The superstrate can be air or a dielectric with refractive index n2. (b) AFM image of a square array of gold nanodisks with D=480nm, d=160nm, and h=50nm. (c) Scanning electron microscopy image of an array of aluminum nanodisks with D=300nm, d=120nm, and h=50nm.

Normal incidence extinction cross-section spectrum calculated with FDTD for a square array of gold nanodisks with diameter d=80nm and thickness h=50nm for different lattice periods (from 300 to 700 nm with a 10 nm step) in a homogeneous dielectric environment (n1=n2=1.5). Solid lines show the theoretical position of Rayleigh anomalies, and the dotted horizontal line is the position of the dipolar resonance from the isolated gold nanodisk.

Normalized electric field modulus maps for different lattice periods. The insets on the top of each of the columns are line cuts of Fig. 2, showing the extinction cross section σext versus wavelength for three different periods: D=300 (left column), D=500nm (center column), and D=650nm (right column). The arrows indicate the wavelengths where the field maps were calculated. (a) FDTD maps of the normalized electric field modulus computed in a plane located at mid-height of the metal nanoparticles for an array with D=300nm at λ=620.3nm. The black arrow denotes the incident polarization. The same field maps were computed for (b) D=500nm and λ=619.9nm; (c) D=500nm and λ=754.8nm; (d) D=650nm and λ=615.1nm; and (e) D=650nm and λ=692.9nm.

Linewidth engineering using lattice modes. (a) Calculated quality factor of the lattice mode of arrays of gold nanodisks as a function of the lattice period for different disk diameters at normal incidence. The dielectric environment is symmetric (n1=n2=1.5). (b) Same, with air as the superstrate (n2=1).

Experimental (a), (c) and simulated (b), (d) dispersion curves of the gold nanodisk arrays for s (a), (b) and p (c), (d) polarizations. The period of the array is D=480nm, and the diameter of the nanodisks is d=180nm. White lines represent the position of the Rayleigh anomalies computed using Eq. (1) with n1=1.52 and n2=1.52 (solid lines) or n2=1 (dotted lines).

Experimental (a), (b) and simulated (c)–(h) dispersion curves of the PMMA-covered gold nanodisk arrays for s and p polarizations. The period of the array is D=480nm, and the diameter of the nanodisks is d=180nm. White lines represent the position of the Rayleigh anomalies computed using Eq. (1) with n1=1.52 and n2=1.52 (solid lines) or n2=1 (dotted lines). The simulations were performed using three different geometries as pictured in the insets: (c), (d) a semi-infinite PMMA superstrate; (e), (f) a 180 nm thick PMMA layer onto the top of the substrate, and (g), (h) a 180 nm thick PMMA standing onto the top of the nanoparticles.

Experimental dispersion curves of PMMA-covered aluminum nanodisk arrays for (a)–(c) s-polarization and (d)–(f) p-polarization. The diameter of the nanoparticles is d=120nm. The period of the array is (a), (d) D=250nm; (b, e) D=300nm; and (c), (f) D=350nm. White lines represent the position of the glass/glass (solid lines) or glass/air (dotted lines), and Rayleigh anomalies were computed using Eq. (1).

Experimental dispersion curve of d=60nm aluminum nanodisk arrays in the ultraviolet for s-polarization. The period of the array is D=260nm. White lines represent the position of the glass/glass (solid lines) or glass/air (dotted lines) Rayleigh anomalies were computed using Eq. (1).